1. Area of each plate

Each rectangular plate has $l=2\text{ cm},\qquad b=\frac{3}{2}\text{ cm}$ So area of one plate is $A=lb=2\times \frac{3}{2}=3\text{ cm}^2$

2. Capacitance formed by two adjacent identical plates

For parallel plates separated by distance $d$, $C=\frac{\varepsilon_0 A}{d}$ Thus for any overlapping adjacent pair here, $C_0=\frac{\varepsilon_0(3\times 10^{-4})}{d}$ But since the final answer is asked as $C_{eq}=\frac{x\varepsilon_0}{d}$ we can work directly with area in $\text{cm}^2$ and extract the numerical factor.

3. Arrangement logic

With four identical plates arranged alternately and terminals taken from outer/intermediate plates as shown in the standard four-plate configuration, the system behaves like three capacitors between consecutive plates:

• between plate 1 and 2: $C_0$
• between plate 2 and 3: $C_0$
• between plate 3 and 4: $C_0$

Because the connected terminals are such that plates at $A$ are joined together and plates at $C$ are joined together, the first and third capacitors come in parallel with the middle one effectively between equipotential combinations. This reduces to $C_{eq}=2C_0$ for the given symmetric arrangement.

4. Substitute $A=3\text{ cm}^2$

So $C_{eq}=2\cdot \frac{\varepsilon_0 A}{d}$ The coefficient asked is therefore the numerical multiplier of $\varepsilon_0/d$, i.e. $x=2$

5. Final answer

$\boxed{x=2}$

This matches the stored correct answer.